Sure, let's go through the steps to find the electric potential at a distance of 4.20 meters from a charge of [tex]\(-3.37 \times 10^{-6} \, \text{C}\)[/tex].
### Step 1: Understanding the Formula
The formula for the electric potential [tex]\( V \)[/tex] due to a point charge [tex]\( Q \)[/tex] at a distance [tex]\( r \)[/tex] is given by:
[tex]\[ V = \frac{k \cdot Q}{r} \][/tex]
where:
- [tex]\( k \)[/tex] is the electrostatic constant, equivalent to [tex]\( \frac{1}{4 \pi \epsilon_0} \)[/tex].
- [tex]\( Q \)[/tex] is the charge.
- [tex]\( r \)[/tex] is the distance from the charge.
### Step 2: Constants and Given Values
- The charge [tex]\( Q \)[/tex] is [tex]\(-3.37 \times 10^{-6} \, \text{C}\)[/tex] (coulombs).
- The distance [tex]\( r \)[/tex] is [tex]\( 4.20 \, \text{m} \)[/tex] (meters).
- The electrostatic constant [tex]\( k \)[/tex] can be calculated from [tex]\( \frac{1}{4 \pi \epsilon_0} \)[/tex] where [tex]\( \epsilon_0 \)[/tex] (the permittivity of free space) is [tex]\( 8.854 \times 10^{-12} \, \text{F/m} \)[/tex].
### Step 3: Arrange the Values into Formula
Given these values, we use the formula to calculate the electric potential [tex]\( V \)[/tex].
### Step 4: Calculate the Electric Potential
After substituting the values into the formula, you obtain:
[tex]\[ V = \frac{1 / (4 \pi \times 8.854 \times 10^{-12}) \times -3.37 \times 10^{-6}}{4.20} \][/tex]
### Step 5: Result and Sign
This calculation results in the electric potential value of approximately:
[tex]\[ V \approx -7211.5933371476885 \, \text{V} \][/tex]
### Conclusion
Thus, the electric potential at a distance of 4.20 meters from a [tex]\(-3.37 \times 10^{-6} \, \text{C}\)[/tex] charge is:
[tex]\[ -7211.6 \, \text{V} \][/tex]
Remember to include the negative sign because the charge is negative. The negative sign indicates that the potential is lower than the reference point (usually considered at infinity where the potential is zero).
